The laser-diode-array (LDA) pumped Yb:YAG thin-disc 1030 nm laser is demonstrated. The Yb:YAG crystal doped with 10% Yb atomic fraction is 420 μm in thickness and 11 mm in diameter. It is mounted onto the micro-channel copper heat sink by Cr/Au/In. The four-pass optical coupling system is well designed with two spherical imaging mirrors (diameter 26 mm, radius of curvature 50 mm). With 32.4 W pump power, the maximum output power of 13.55 W at 1030 nm is obtained. The optical-optical conversion efficiency is 41.8%.